Where is your Photos Library stored? Is it on your System drive in the Pictures folder or on a different drive?
The error message you are seeing can also indicate a problem with the format off the file system of the external drive. If the file system on the external drive is not the same as the file system format you are copying from, you may not be able to copy some files in the library, because the filenames cannot be recreated on the destination drive.
Check the file system on the external drive, if it is MacOS Extended (Journaled) like the internal drive of the Mac.
You can see the file system format in the info panel, if you select the drive in the Finder and enter ⌘I .
It may be also a permissions problem.
- Set the "ignore Ownership on this volume" flag for your external drive.
- You can change the permissions for all photos at once in the Finder.
- Select the enclosing folder of your Photos Library in the Finder and use the command "File > Get Info".
- In the Info panel click the disclosure triangle beside "Sharing and permissions". Click the padlock icon too unlock it with your admin password.
- Now check, if the permissions are set correctly and change them to give yourself read&write permissions.
- Then click the gears icon at the bottom to open the Actions menu and click "Apply to enclosed items".
- This will set the permissions for all items in the subfolders to the same permissions.

- If the Library cannot be read, and the file system on the destination drive is correct, but you can still not copy, one of the files inside may be corrupted and cannot be read. Then try to copy the library in parts. This way, you are able to identify the culprit that is causing the I/O error and can skip it, when copying:
Create a new folder on your external drive. Call it "Photos Library Copy".
Ctrl-click (or right-click) your current Photos Library and use the command "Show Package Contents". This will open a folder, showing you the files and folders inside your Photos Library.
Copy these folders one-by-one to to the new folder on your external drive. If one of these folders is giving an error -36, check how far the copying proceeded. The files, that have been copied, are o.k. The file or folder, that should have been copied next will be the unreadable file. Probably the problem is caused by one of the files in "Masters" or a database folder. In that case look into the Masters folder and copy as much as you can, while leaving out the file that will not copy.
When you are done, rename the copy of your Photos Library to "Photos Library Copy.photoslibrary" and double click it to open it in Photos. Can Photose open this library?